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Q. 103

Expert-verifiedFound in: Page 430

Book edition
6th

Author(s)
Daren Starnes, Josh Tabor

Pages
837 pages

ISBN
9781319113339

Lefties Refer to Exercise 99.

a. Justify why L can be approximated by a Normal distribution.

b. Use a Normal distribution to estimate the probability that 15 or more students in the sample are left-handed.

- The $L$ is about regularly distributed.
- The resultant probability is $0.1003.$

The number of students $\left(n\right)=100$

Left-handed students as a percentage of total students $\left(p\right)=0.11$

Consider,

$np=100(0.11)=11>10\phantom{\rule{0ex}{0ex}}n(1-p)=100(1-0.11)=89>10$

Therefore, the L is about regularly distributed.

The number of students $\left(n\right)=100$

Left-handed students as a percentage of total students$\left(p\right)=0.11$

If 15 or more pupils are left-handed, the probability is calculated as"

$\begin{array}{rcl}P(X& \ge & 15)=P\left(Z\ge \frac{15-100(0.11)}{\sqrt{100(0.11)(1-0.11)}}\right)\\ & =& P(Z\ge 1.28)\\ & =& 1-0.8997\\ & =& 0.1003\end{array}$Thus, the resultant probability is 0.1003.

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